Great Students,
Greetings to everyone.
To ensure a safe learning environment for everyone and a high academic standard for teaching and learning, I ask everyone to please follow these requirements.
(1.) Please review the Rules of Netiquette.
(2.) Each post should be unique and substantive. Please be creative.
(a.) The post should be on-topic as asked in the Discussion assessment.
(b.) There are several concepts/topics discussed each week as listed in the Pacing Guides.
When applicable, post on a different concept/topic that has not been posted by someone else, provided it is a topic/concept listed for that week.
(c.) Review all previous posts from your colleagues and my comments to their posts/responses as applicable, before you submit your own post.
(d.) Unless stated otherwise, all DB posts besides DB 1 are applied problems. We want our students to see the meaning of what they are learning. We want them to relate their learning
to real-world applications. In that regard, please post an application of the topic/concept. Review your
textbook (eText), solve an applied problem, check the solution at the back
of the textbook to ensure you got it correct. Then, submit your post by writing the applied problem completely, solving it by showing all work, and
interpreting your solution (Write – Solve – Interpret).
Please see the DB Samples for examples of substantive posts.
(e.) As specified in the DB Samples, please write:
(i.) Topic
(ii.) Concept
(iii.) Applied Problem (please note that all word problems are not applied problems. Contact me via school email if you need assistance with finding an applied problem)
(iv.) Solution
(v.) Interpretation/Conclusion/Decision (whichever is applicable)
(vi.) Reference
(3.) (a.) The initial post is typically due on Thursday each week by 11:59 pm EDT.
(b.) Please make only one initial post. In other words, only one thread per student is allowed.
(c.) Multiple posts/threads are not allowed and will not be graded.
(d.) Re-posts are allowed and may be needed based on my comments to your initial post.
(e.) If you need to do a re-post, please post it as a response to my comments or as a response to your first post as applicable. But, please do not create a new thread.
(f.) I am not required to comment on every post. However, if I make any comment to your post, please make sure you address that comment as applicable.
(g.) If you do not understand my comments, please contact me via email and/or attend the Live Sessions/Office Hours. Typically, I do not go back-and-forth with a student
(responding more than one time to a student) in DB forums. Hence, it is highly recommended you contact me via email if you have any question regarding my comments.
(h.) If any of your colleagues or I make a comment to your initial post, please do not edit/modify that post after we make the comment. Rather, respond
to the comment as applicable.
(4.) (a.) The initial response (response to an initial post) is typically due on Saturday each week by 11:59 pm EDT.
(b.) In your response, please mention the first name of your colleague.
(c.) At least one response (one or more responses) to an initial post of your colleagues is required.
(d.) Please write a substantive response.
A substantive response is the response that provides constructive criticism, alternative approach that gives the same correct output, additional helpful information that will improve the post,
and the correction of any incorrect step and/or output among others.
How would you improve the initial post?
Did you find any errors in the initial post? If you do, please correct the error. Teach your colleague about the error, and explain to him/her how to fix it.
What new knowledge can your colleague acquire from you based on your response?
Can you solve the initial post using an alternative approach that will give the same correct output?
What real-world examples/applications can you provide based on the initial post? Discuss/Explain. Do not just state/mention. Cite your sources accordingly.
Did your colleague learn anything meaningful from you based on your response to the initial post?
Please focus on the initial post. Do not deviate from the concept/topic in the initial post. Do not bring up your own unrelated topic/concept.
Teach/Show your colleague something new and meaningful based on the initial post.
Please see the DB Samples for examples of substantive responses.
(5.) (a.) Any attachment should be inserted directly (not attached). Any attachment whose content is not entirely seen directly in the Canvas editor will not be graded.
This implies that no one should click your attachment to see it. Insert it directly so everyone can clearly see it. Please see (b.) below.
(b.) For all Math work (symbols, formulas, equations, fractions, radicals and exponents among others); please use the Insert Math Equation icon.
(c.) Alternatively, if your handwriting is legible; you can write your post/response on paper, take clear pictures of the entire work and insert directly in the Canvas editor.
Do not attach as a file. Insert directly in the editor as a picture.
Use the Snipping Tool or the Snip & Sketch on your computer to take clear screenshots and trim off excess space/irrelevant information, then insert the screenshots directly
in the Canvas editor.
(6.) (a.) For DB 2 through DB 14 assessment: written and/or video submissions are acceptable.
For DB 1 and DB 15 assessment: written submission is required.
(b.) Written submission:
Use an acceptable font and font size (at least a font size of 12pt) in all your writings.
Times New Roman font and a font size of 14pt is highly recommended.
(c.) Video submission:
(I.) Closed-captioning of your video is required.
(II.) Please insert the video directly in the Canvas editor. Do not post an attachment.
(d.) Written and/or Video submissions:
(I.) Make sure your post and response are well-formatted (visually appealing), nice background/lighting, etc.
(II.) Insert any diagrams/visuals directly in the Canvas editor. Label them accordingly. If they are not drawn to scale, please
make a note in that regard as applicable.
(III.) Do not attach any file.
(IV.) If you need to Include any link in your post and/or response, please paste the direct address of that link.
(7.) Please proof-read your writings for mechanical accuracy errors.
Any use of "i" attracts deduction of points.
Multiple mechanical accuracy errors will lead to deduction of points.
I understand that this is not an English class. However, you are expected to write well.
(8.) Sources must be cited accordingly.
You may use the: APA (American Psychological Association) style, MLA (Modern Language Association) style, or the Chicago Manual of Style.
(9.) Please review the Sample Discussion Post and Response.
(10.) Please review the Discussion Board Rubric.
Should you have any questions, please let me know.
Thank you.
Samuel Chukwuemeka
Working together for success
Sample 1:
Example Post
Topic: Solving Problems and Explaining Solutions
Concept: Critical Thinking
Word Problem/Application:
Thomas stood on the middle rung of a ladder.
He climbed up 3 rungs, moved down 5 rungs, and then climbed up 7 rungs.
Then he climbed up the remaining 2 rungs to the top of the ladder.
(a.) How many rungs are above the middle rung of the ladder?
(b.) How many rungs are below the middle rung of the ladder?
(c.) How many rungs are there in the whole ladder?
Solution:
Quantitative Reasoning Approach:
Climbing up is positive
Climbing down is negative
Initial position = middle rung = 0
He climbed up 3 rungs = 3
moved down 5 rungs = −5
climbed up 7 rungs = 7
climbed up the remaining 2 rungs = 2
This implies: 0 + 3 − 5 + 7 + 2 = 7
Top = 7th rung
(a.) There are 7 rungs above the middle rung of the ladder
(b.) Similarly, there are 7 rungs below the middle rung of the ladder
(c.) The total number of rungs = 7 rungs + middle rung + 7 rungs = 7 + 1 + 7 = 15 rungs.
Interpretation/Conclusion/Decision:
Because there are 7 rungs above the middle rung, and 7 rungs below the middle rung; including the middle rung, there are 15 rungs.
Reference:
Chukwuemeka, Samuel (2023). Critical Thinking, Reasoning/Argument, Problem Solving. Retrieved July 27, 2023, from https://quantitativereasoning.appspot.com/LogicReasoning/CriticalThinking.html
Example Response
Samuel, you explained the solution well. You used the Quantitative Reasoning approach.
We can solve the question using another approach: Diagrammatic/Graphical Approach:
We can represent the information on a diagram. This approach is especially useful for visual learners.
The total number of rungs = 7 rungs above Middle rung + 7 rungs below Middle rung + Middle rung = 15 rungs.
Sample 2:
Example Post
Topic: Measures of Center (Linear and Other Relationships)
Concept: Grade Point Average (GPA)
Word Problem/Application:
At the end of the second semester, Rita earned an A in the 4-credit Algebra course, a B in the 3-credit English course,
a B in the 4-credit Biology course, an A in the 4-credit Chemistry course, and a C in the 1-credit Chinese Language course.
Using a 4-point grade system, A is equivalent to 4 points, B is equivalent to 3 points, C is equivalent to 2 points, D is equivalent to 1 point, and F has no point.
Calculate Rita's grade point average (GPA) for the second semester.
Solution:
Let us represent this information in a table.
Course | Grade | Point | Credit Hour (CH) | Grade Point (GP) = Point * CH |
---|---|---|---|---|
Algebra | A | 4 | 4 | 4 * 4 = 16 |
English | B | 3 | 3 | 3 * 3 = 9 |
Biology | B | 3 | 4 | 3 * 4 = 12 |
Chemistry | A | 4 | 4 | 4 * 4 = 16 |
Chinese | C | 2 | 1 | $2 * 1 = 2$ |
$\Sigma CH = 16$ | $\Sigma GP = 55$ |
Interpretation/Conclusion/Decision:
Rita's grade point average for the second semester is 3.44.
Reference:
Chukwuemeka, Samuel (2023). Measures of Central Tendency. Retrieved June 26, 2023, from https://statistical-science.appspot.com/DescriptiveStatistics/measuresCenter.html
Example Response
Nice work, Samuel.
The use of the table makes for easier comprehension.
Let's assume Rita already knows her grades in Algebra, English, Biology, and Chemistry, but does not know her grade in
Chinese.
She wants a GPA of at least 3.44.
What is the minimum grade that she make in Chinese to make at least a GPA of 3.44 for the second semester?
Let the point that she needs to make in the Chinese course be x
We do not know the grade but when we find the point, it will help determine the grade.
May I use your table?
Course | Grade | Point | Credit Hour (CH) | Grade Point (GP) = Point * CH |
---|---|---|---|---|
Algebra | A | 4 | 4 | 4 * 4 = 16 |
English | B | 3 | 3 | 3 * 3 = 9 |
Biology | B | 3 | 4 | 3 * 4 = 12 |
Chemistry | A | 4 | 4 | 4 * 4 = 16 |
Chinese | $x$ | $x$ | 1 | $x * 1 = x$ |
$\Sigma CH = 16$ | $\Sigma GP = 53 + x$ |
At least a GPA of 3.44 means: ≥ 3.44
$
\implies \\[3ex]
\dfrac{53 + x}{16} \ge 3.44 \\[5ex]
53 + x \ge 16(3.44) \\[3ex]
53 + x \ge 55.04 \\[3ex]
x \ge 55.04 - 53 \\[3ex]
x \ge 2.04 \\[3ex]
$
A point of at least 2.04 means a C and above.
Rita needs to make at least a C grade in the Chinese course to earn a GPA of 3.44
Sample 3:
Example Post
Topic: Linear Functions
Concept: Slope
Word Problem/Application:
In January 2004, the price of a gallon of milk was $3.30 per gallon.
In January 2015, the price was $3.76 per gallon.
Calculate the average rate of change in the price of a gallon of milk from 2004 to 2015.
Interpret your solution.
(Source: United States Department of Labor).
Solution:
The average rate of change is also known as the slope.
From the information, we see that the input is the year and the output is the price
of a gallon of milk.
Student: How did you know?
Teacher: What variable depends on what variable? Does the price of milk depend on
the year, or does the year depend on the price of milk?
Student: The price of milk depends on the year.
Teacher: That is correct. This means that the price of milk is the ...
Student: Dependent variable also known as the output or the $y-value$
Teacher: That is correct. The year is the ...
Student: Independent variable also known as the input or the $x-value$
Teacher: Correct. Another reason is the based on the wording of the question:
it asked for the average rate of change in the "price" based on the "year"
This means the changes in the output based on the changes in the input.
That describes the slope.
$
Point\:1 = (2004, 3.30) \\[3ex]
x_1 = 2004 \\[3ex]
y_1 = 3.30 \\[3ex]
Point\:2 = (2015, 3.76) \\[3ex]
x_2 = 2015 \\[3ex]
y_2 = 3.76 \\[3ex]
m = \dfrac{y_2 - y_1}{x_2 - x_1} \\[5ex]
where: \\[3ex]
m = slope \\[3ex]
x_1 = initial\;\;x-value \\[3ex]
y_1 = initial\;\;y-value \\[3ex]
x_2 = new\;\;x-value \\[3ex]
y_2 = new\;\;y-value \\[3ex]
m = \dfrac{3.76 - 3.30}{2015 - 2004} \\[5ex]
= \dfrac{0.46}{11} \\[5ex]
= 0.041818182 \\[3ex]
$
Interpretation/Conclusion/Decision:
The average rate of change in the price of a gallon of milk from 2004 to 2015 is
about $0.0418 per year.
This means that there was an increase of about $0.04 (4 cents) in
the price of a gallon of milk per year from 2004 to 2015
Reference:
Chukwuemeka, Samuel (2018). Word Problems on Linear Functions. Retrieved May 12, 2023, from https://precalculus.appspot.com/RelationsFunctions/linearFunctionsApplications.html
Example Response
Samuel, you did well in your work.
We can check your interpretation to ensure it is correct.
Check the Interpretation
Use the exact (not approximate) values of the slope.
$
2004:\:\:Price = \$3.30 \\[3ex]
2005:\:\:Price \approx 3.30 + 0.041818182 = 3.341818182 \\[3ex]
2006:\:\:Price \approx 3.341818182 + 0.041818182 = 3.38363636 \\[3ex]
2007:\:\:Price \approx 3.38363636 + 0.041818182 = 3.42545454 \\[3ex]
2008:\:\:Price \approx 3.42545454 + 0.041818182 = 3.46727272 \\[3ex]
2009:\:\:Price \approx 3.46727272 + 0.041818182 = 3.5090909 \\[3ex]
2010:\:\:Price \approx 3.5090909 + 0.041818182 = 3.55090908 \\[3ex]
2011:\:\:Price \approx 3.55090908 + 0.041818182 = 3.59272726 \\[3ex]
2012:\:\:Price \approx 3.59272726 + 0.041818182 = 3.63454544 \\[3ex]
2013:\:\:Price \approx 3.63454544 + 0.041818182 = 3.67636362 \\[3ex]
2014:\:\:Price \approx 3.67636362 + 0.041818182 = 3.7181818 \\[3ex]
2015:\:\:Price \approx 3.7181818 + 0.041818182 = \$3.75999998 \approx \$3.76
$
Criteria | Ratings | Points | ||
---|---|---|---|---|
Post |
50 to > 40.0 pts Proficient Post is substantive, on-topic, and submitted on time. |
40 to > 25.0 pts Fair Post is substantive, and on-topic, but not submitted on time; and/or Post is not substantive and on-topic, but submitted on time. |
25 to > 0 pts Novice No post was submitted; and/or Post is not substantive; and/or Post is partly substantive but not submitted on time; and/or Post is off-topic. |
50 pts |
Response |
30 to > 24.0 pts Proficient Response is substantive. |
24 to > 15.0 pts Fair Response is not substantive. |
15 to > 0 pts Novice No response was submitted; and/or Response is not substantive. |
30 pts |
Requirements |
20 to > 16.0 pts Proficient All DB requirements were followed; or Some DB Requirements were followed. |
16 to > 10.0 pts Fair Some DB Requirements were followed. |
10 to > 0 pts Novice Some DB Requirements were followed; or No DB Requirement was followed. |
20 pts |
Total Points: 100 |
Post:
May you please number your responses to these questions?
(1.) Please write a brief introduction of yourself.
Include whatever you want us to know about you.
(2.) Please click the Modules link located on the Left Hand Side in the Canvas course.
Review all the information in the Getting Started module.
How many items/sections are listed in that module?
(3.) There are two videos listed in the Getting Started module.
Have you reviewed the two videos?
If yes, do you understand it?
If no, please review before you continue.
(4.) Do you have access to a working computer (laptop/desktop only; not a smartphone, not a tablet, not an iPad, not a Chromebook) with Internet connection to complete the course successfully?
A Chromebook may be used to complete MyLab Math (MLM) assignments. However, you cannot use a Chromebook to complete the project.
(5.) Have you reviewed the course syllabus?
If yes, do you understand it?
If no, please review before you continue.
(6.) Have you registered for the MyLab Math (MLM) assignments?
If yes, have you started work on an assignment?
If no, please stop now. Go and register now. Attempt at least one question before you continue.
(7.) Have you reviewed the Discussion Board (DB) Forum requirements?
If yes, do you understand it?
If no, please review before you continue.
(8.) Have you reviewed the Discussion Board (DB) Post and Response samples?
If yes, do you understand it?
If no, please review before continuation.
(9.) Have you reviewed the Discussion Board rubric?
If yes, do you understand it?
If no, please review it before you continue.
(10.) (a.) How many types of graded assessments are there for this course?
(b.) What is the weight of each type of assessment?
(c.) Do you know how your MLM grades are calculated?
(d.) Do you know how to calculate your current course grade?
(e.) Do you know how to calculate your final course grade?
(11.) (a.) Have you reviewed the Welcome announcement?
If no, please review it before continuation.
(b.) If yes, what are the days and times for the Live Sessions/Office Hours?
(c.) If the days and times do not suit your schedule and you need to ask questions and/or contact the Instructor, what should you do?
(12.) Besides the Instructor Office Hours/Live Sessions, what are the other tutoring opportunities available to you?
Please list them.
(13.) Have you reviewed the Pacing Guide?
If no, please review before you continue.
If yes, do you understand it?
(14.) Do you understand that:
(a.) This course will require a lot of your time.
(b.) You will do a lot of work on your own in this course.
(15.) (a.) Have you reviewed the Frequently Asked Questions (FAQs)?
If no, please review before you continue.
If yes, do you understand it?
(b.) Can you think of any question you have at the moment that you would like it to be addressed/answered?
If yes, please state so.
If no, please state so.
(More questions will be updated as needed, as we progress through the course.)
Response:
May you please number your responses to these questions?
(1.) Please review the brief introduction of your colleague.
Based on the introduction, say something nice to your colleague.
(2.) Please review the entire post of your colleague.
Advise your colleague on how to successfully complete the course.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned last week or this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Discuss a real-world application of any of the concepts/topics assigned this week or next week.
You may write an applied problem and solve it, or you may write a paper regarding the application.
(2.) Then, please respond to the initial post of any of your colleagues.
Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Sample)
(c.) Discussion Assessment Rubric
(1.) Then, please post:
Write a one-page summary (minimum of 250 words) of what you have learned in the class.
Please review your writings.
Give specific examples.
(2.) Then, please respond to the initial post of any of your colleagues.